《统计学》第五版总复习.ppt

* * * * * * 65 The sampling distribution is a function of the sample sizes upon which the sample variances are based. Hint: Recall the formula for variance! s2 = S(x -`x)2/(n-1) As a result of this class, you will be able to ... An estimator is a random variable used to estimate a population parameter (characteristic). Unbiasedness An estimator is unbiased if the mean of its sampling distribution is equal to the population parameter. Efficiency The efficiency of an unbiased estimator is measured by the variance of its sampling distribution. If two estimators, with the same sample size, are both unbiased, then the one with the smaller variance has greater relative efficiency. Consistency An estimator is a consistent estimator of a population parameter if the larger the sample size, the more likely it is that the estimate will come close to the parameter. An estimator is a random variable used to estimate a population parameter (characteristic). Unbiasedness An estimator is unbiased if the mean of its sampling distribution is equal to the population parameter. Efficiency The efficiency of an unbiased estimator is measured by the variance of its sampling distribution. If two estimators, with the same sample size, are both unbiased, then the one with the smaller variance has greater relative efficiency. Consistency An estimator is a consistent estimator of a population parameter if the larger the sample size, the more likely it is that the estimate will come close to the parameter. 10.1 方差分析概述 3. 误差分析 如果不同的水平对观测结果没有影响 组间误差中只包含有随机误差，没有系统误差 组间方差与组内方差很接近，二者比值接近1 如果不同的水平对观察结果有影响 组间误差中包含随机误差和系统误差 组间方差大于组内方差，二者比值就会大于1 当这个比值大到某种程度时，不同水平之间存在着显著差异，即自变量对因变量有影响 小结：方差分析表的一般形式 H0：μ1= μ2 =…=μk H1：k个总体均值不全相等 检验统计量 其中MSA=SSA/(k-1)； MSE=SSE/(n–k) 拒绝规则 P值法：P小于等于a，则拒绝原假设 临界值法：F大于等于Fa，则拒绝原假设 其中Fa是分子自由度为k-1、分母自由度为n-k的F分布右侧（上侧）面积为a的F值 3. 统计决策 如果原假设H0：μ1= μ2 =…=μk成立，则表明没有系统误差，组间方差MSA与组内方差MSE的比值差异不会太大；如果MSA显著大于MSE，说明各水平（总体）之间的差异显然不仅仅有随机误差，还有系统误差 判断因素的水平是否对其观测值有显著影响